Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Addressing the net balances problem as a prerequisite for EU budget reform: a proposal

Conflict among member states regarding the distribution of net financial burdens has been allowed to contaminate the entire design of the EU budget with very negative consequences in terms of equity, efficiency and transparency. To get around this problem and pave the way for a substantive budget reform, we propose to decouple distributional negotiations from the rest of the budget process by linking member state net balances in a rigid manner to relative prosperity. This would be achieved through the introduction of a system of compensating horizontal transfers that would take to its logical conclusion the Commission's proposal for a generalized compensation mechanism. We discuss the impact of the proposed scheme on member states? incentives and illustrate its financial implications using revenue and expenditure projections for 2013 that are based on the current Financial Perspectives and Own Resources Decision.

Orbit decidability and the conjugacy problem for some extensions of groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

The generic Hanna Neumann conjecture and post correspondence problem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

Expectations, Learning and Monetary Policy: An Overview of Recent Research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents’ learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

Can Migrants save Greece from Ageing? A Computable General Equilibrium Approach using G-AMOS.

The population of Greece is projected to age in the course of the next three decades. This paper combines demographic projections with a multi-period economic Computable General Equilibrium (CGE) modelling framework to assess the macroeconomic impact of these future demographic trends. The simulation strategy adopted in Lisenkova et. al. (2008) is also employed here. The size and age composition of the population in the future depends on current and future values of demographic parameters such as the fertility, mortality rates and the level of annual net migration. We use FIV-FIV software in order to project population changes for 30 years. Total population and working age population changes are introduced to the GAMOS modelling framework calibrated for the Greek economy for the year 2004. Positive net migration is able to cancel the negative impacts of an ageing population that would otherwise occur as a result of the shrinking of the labour force. The policy implication is that a viable, long-lasting migration policy should be implemented, while the importance of policies that could increase fertility should also be considered.

A computable general equilibrium analysis of the relative price sensitivity required to induce rebound effects in response to an improvement in energy efficiency in the UK economy

In recent years there has been extensive debate in the energy economics and policy literature on the likely impacts of improvements in energy efficiency. This debate has focussed on the notion of rebound effects. Rebound effects occur when improvements in energy efficiency actually stimulate the direct and indirect demand for energy in production and/or consumption. This phenomenon occurs through the impact of the increased efficiency on the effective, or implicit, price of energy. If demand is stimulated in this way, the anticipated reduction in energy use, and the consequent environmental benefits, will be partially or possibly even more than wholly (in the case of ‘backfire’ effects) offset. A recent report published by the UK House of Lords identifies rebound effects as a plausible explanation as to why recent improvements in energy efficiency in the UK have not translated to reductions in energy demand at the macroeconomic level, but calls for empirical investigation of the factors that govern the extent of such effects. Undoubtedly the single most important conclusion of recent analysis in the UK, led by the UK Energy Research Centre (UKERC) is that the extent of rebound and backfire effects is always and everywhere an empirical issue. It is simply not possible to determine the degree of rebound and backfire from theoretical considerations alone, notwithstanding the claims of some contributors to the debate. In particular, theoretical analysis cannot rule out backfire. Nor, strictly, can theoretical considerations alone rule out the other limiting case, of zero rebound, that a narrow engineering approach would imply. In this paper we use a computable general equilibrium (CGE) framework to investigate the conditions under which rebound effects may occur in the Scottish regional and UK national economies. Previous work has suggested that rebound effects will occur even where key elasticities of substitution in production are set close to zero. Here, we carry out a systematic sensitivity analysis, where we gradually introduce relative price sensitivity into the system, focusing in particular on elasticities of substitution in production and trade parameters, in order to determine conditions under which rebound effects become a likely outcome. We find that, while there is positive pressure for rebound effects even where (direct and indirect) demand for energy is very price inelastic, this may be partially or wholly offset by negative income and disinvestment effects, which also occur in response to falling energy prices.

A comparison of results from MRIO and interregional computable general equilibrium (CGE) analyses of the impacts of a positive demand shock on the ‘CO2 trade balance’ between Scotland and the rest of the UK

In previous work we have applied the environmental multi-region input-output (MRIO) method proposed by Turner et al (2007) to examine the ‘CO2 trade balance’ between Scotland and the Rest of the UK. In McGregor et al (2008) we construct an interregional economy-environment input-output (IO) and social accounting matrix (SAM) framework that allows us to investigate methods of attributing responsibility for pollution generation in the UK at the regional level. This facilitates analysis of the nature and significance of environmental spillovers and the existence of an environmental ‘trade balance’ between regions. While the existence of significant data problems mean that the quantitative results of this study should be regarded as provisional, we argue that the use of such a framework allows us to begin to consider questions such as the extent to which a devolved authority like the Scottish Parliament can and should be responsible for contributing to national targets for reductions in emissions levels (e.g. the UK commitment to the Kyoto Protocol) when it is limited in the way it can control emissions, particularly with respect to changes in demand elsewhere in the UK. However, while such analysis is useful in terms of accounting for pollution flows in the single time period that the accounts relate to, it is limited when the focus is on modelling the impacts of any marginal change in activity. This is because a conventional demand-driven IO model assumes an entirely passive supply-side in the economy (i.e. all supply is infinitely elastic) and is further restricted by the assumption of universal Leontief (fixed proportions) technology implied by the use of the A and multiplier matrices. In this paper we argue that where analysis of marginal changes in activity is required, a more flexible interregional computable general equilibrium approach that models behavioural relationships in a more realistic and theory-consistent manner, is more appropriate and informative. To illustrate our analysis, we compare the results of introducing a positive demand stimulus in the UK economy using both IO and CGE interregional models of Scotland and the rest of the UK. In the case of the latter, we demonstrate how more theory consistent modelling of both demand and supply side behaviour at the regional and national levels affect model results, including the impact on the interregional CO2 ‘trade balance’.

Outsourcing versus FDI in oligopoly equilibrium

We consider the make-or-buy decision of oligopolistic firms in an industry in which final good production requires specialised inputs. Factor price considerations dictate that firms acquire the intermediate abroad, by either producing it in a wholly owned subsidiary or outsourcing it to a supplier who must make a relationship specific investment. Firms’ internationalisation mode depends on cost and strategic considerations. Crucially, asymmetric equilibria emerge, with firms choosing different modes of internationalisation, even when they are ex-ante identical. With ex-ante asymmetries, lower cost producers have a stronger incentive to vertically integrate (FDI), while higher cost firms are more likely to outsource.

The added value from adopting a CGE approach to analyse changes in environmental trade balances

The application of multi-region environmental input-output (IO) analysis to the problem of accounting for emissions generation (and/or resource use) under different accounting principles has become increasingly common in the ecological and environmental economics literature in particular, with applications at the international and interregional subnational level. However, while environmental IO analysis is invaluable in accounting for pollution flows in the single time period that the accounts relate to, it is limited when the focus is on modelling the impacts of any marginal change in activity. This is because a conventional demand-driven IO model assumes an entirely passive supply-side in the economy (i.e. all supply is infinitely elastic) and is further restricted by the assumption of universal Leontief (fixed proportions) technology implied by the use of the A and multiplier matrices. Where analysis of marginal changes in activity is required, extension from an IO accounting framework to a more flexible interregional computable general equilibrium (CGE) approach, where behavioural relationships can be modelled in a more realistic and theory-consistent manner, is appropriate. Our argument is illustrated by comparing the results of introducing a positive demand stimulus in the UK economy using IO and CGE interregional models of Scotland and the rest of the UK. In the case of the latter, we demonstrate how more theory consistent modelling of both demand and supply side behaviour at the regional and national levels effect model results, including the impact on the interregional CO2 ‘trade balance’.

The Rebound Effect with Energy Production: A Partial Equilibrium Analysis

Rebound is the extent to which improvements in energy efficiency fail to translate fully into reductions in energy use because of the implicit fall in the price of energy, when measured in efficiency units. This paper discusses aspects of the rebound effect that are introduced once energy is considered as a domestically produced commodity. A partial equilibrium approach is adopted in order to incorporate both energy use and production in a conceptually tractable way. The paper explores analytically two interesting results revealed in previous numerical simulations. The first is the possibility that energy use could fall by more than the implied improvement in efficiency. This corresponds to negative rebound. The second is the finding that the short-run rebound value can be greater than the corresponding long-run value.